The correlation between two variables describes the likelihood that a change in one variable will cause a proportional change in the other variable. A high correlation between two variables suggests they share a common cause or a change in one of the variables is directly responsible for a change in the other variable. Pearson's r value is used to quantify the correlation between two discrete variables.
Label the variable that you believe is causing the change to the other variable as x (the independent variable) and the other variable y (the dependent variable).
Construct a table with five columns and as many rows as there are data points for x and y. Label the columns A through E from left to right.
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Fill in each row with the following values for each (x,y) data point in the first column -- the value of x in Column A, the value of x squared in Column B, the value of y in Column C, the value of y squared in Column D and the value x times y in Column E.
Make a final row at the very bottom of the table and put the sum of all the values of each column in its corresponding cell.
Compute the product of the final cells in Column A and C.
Multiply the final cell in Column E by the number of data points.
Subtract the value obtained in Step 5 from the value obtained in Step 6 and underline the answer.
Multiply the final cell of Column B by the number of data points. Subtract from this value the square of the value of the final cell of Column A.
Multiply the final cell of Column D by the number of data points and subtract the square of the value of the final cell of Column C.
Multiply the values found in Step 8 and 9 together and then take the square root of the result.
Divide the value obtained in Step 7 (it should be underlined) by the value obtained in Step 10. This is Pearson's r, also known as the correlation coefficient. If r is close to 1, there is a strong positive correlation. If r is close to -1, there is a strong negative correlation. If r is close to 0, there is a weak correlation.